Some Remarks on Results Related to ∇-Convex Function | Zendy

Asif R. Khan | Zendy; Faraz Mehmood | Zendy; Faisal Nawaz | Zendy; Aamzir | Zendy

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Some Remarks on Results Related to ∇-Convex Function

Author(s) -

Asif R. Khan,

Faraz Mehmood,

Faisal Nawaz,

Aamzir

Publication year - 2021

Publication title -

journal of mathematical and fundamental sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.216

H-Index - 12

eISSN - 2337-5760

pISSN - 2338-5510

DOI - 10.5614/j.fund.math.sci.2021.53.1.5

Subject(s) - generalization , mathematics , differentiable function , convex function , order (exchange) , type (biology) , pure mathematics , regular polygon , mean value theorem (divided differences) , value (mathematics) , function (biology) , mathematical analysis , statistics , fixed point theorem , picard–lindelöf theorem , economics , ecology , geometry , finance , evolutionary biology , biology

In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented.

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